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<span class="kw">let </span><font color="Maroon" title="c1">G</font> be   <a href="topgrp_1.html#V4" title="TOPGRP_1:attr.4">BinContinuous</a>  <a href="topgrp_1.html#NM4" title="TOPGRP_1:NM.4">TopGroup</a>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide">  for <font color="Olive" title="b1">a</font> being   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font> holds  <font color="Olive" title="b1">a</font> <a href="topgrp_1.html#K1" title="TOPGRP_1:func.1">*</a>  is    <a href="topgrp_1.html#M3" title="TOPGRP_1:mode.3">Homeomorphism</a> of <font color="Maroon" title="c1">G</font></span><br/><span class="kw">let </span><font color="Maroon" title="c2">a</font> be   <a href="struct_0.html#NM1" title="STRUCT_0:NM.1">Element</a> of <font color="Maroon" title="c1">G</font>; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <font color="Maroon" title="c2">a</font> <a href="topgrp_1.html#K1" title="TOPGRP_1:func.1">*</a>  is    <a href="topgrp_1.html#M3" title="TOPGRP_1:mode.3">Homeomorphism</a> of <font color="Maroon" title="c1">G</font></span><br/>



<span class="kw">set </span><font color="Maroon" title="c3">f</font> = <font color="Maroon" title="c2">a</font> <a href="topgrp_1.html#K1" title="TOPGRP_1:func.1">*</a> ;<br/>
<span class="kw">thus </span><a NAME="E1:79"/>
(  <a href="relset_1.html#K1" title="RELSET_1:func.1">dom</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="topgrp_1.html#K1" title="TOPGRP_1:func.1">*</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">G</font> &amp;  <a href="relset_1.html#K2" title="RELSET_1:func.2">rng</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="topgrp_1.html#K1" title="TOPGRP_1:func.1">*</a></span>)</span> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="struct_0.html#K2" title="STRUCT_0:func.2">[#]</a> <font color="Maroon" title="c1">G</font> &amp; <font color="Maroon" title="c2">a</font> <a href="topgrp_1.html#K1" title="TOPGRP_1:func.1">*</a>  is  <a href="funct_1.html#V2" title="FUNCT_1:attr.2">one-to-one</a>  )
 <span class="kw">by</span> <span class="lab"><a class="ref" href="funct_2.html#D1" onmouseover="rs('funct_2/D1')" onmouseout="rh()">FUNCT_2:def 1</a>, <a class="ref" href="funct_2.html#D3" onmouseover="rs('funct_2/D3')" onmouseout="rh()">FUNCT_2:def 3</a></span>; <span class="comment"><font color="firebrick">:: according to </font></span><a class="ref" href="tops_2.html#D5" onmouseover="rs('tops_2/D5')" onmouseout="rh()">TOPS_2:def 5</a>,<a class="ref" href="topgrp_1.html#D4" target="_self" onmouseover="rs('topgrp_1/D4')" onmouseout="rh()">TOPGRP_1:def 4</a> <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> ( <font color="Maroon" title="c2">a</font> <a href="topgrp_1.html#K1" title="TOPGRP_1:func.1">*</a>  is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  &amp; <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="topgrp_1.html#K1" title="TOPGRP_1:func.1">*</a></span>)</span> <a href="tops_2.html#K2" title="TOPS_2:func.2">/"</a>  is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a>  )</span><br/>

<span class="kw">thus </span><a NAME="E2:79"/>
<font color="Maroon" title="c2">a</font> <a href="topgrp_1.html#K1" title="TOPGRP_1:func.1">*</a>  is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="topgrp_1.html#K1" title="TOPGRP_1:func.1">*</a></span>)</span> <a href="tops_2.html#K2" title="TOPS_2:func.2">/"</a>  is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> </span><br/>

<a NAME="E3:79"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="topgrp_1.html#K1" title="TOPGRP_1:func.1">*</a></span>)</span> <a href="tops_2.html#K2" title="TOPS_2:func.2">/"</a>  <a href="funct_2.html#R2" title="FUNCT_2:pred.2">=</a> <span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="group_1.html#K2" title="GROUP_1:func.2">"</a></span>)</span> <a href="topgrp_1.html#K1" title="TOPGRP_1:func.1">*</a> 
 
<span class="kw">by</span> <span class="lab"><a class="ref" href="topgrp_1.html#T18" target="_self" onmouseover="rs('topgrp_1/T18')" onmouseout="rh()">Th17</a></span>;<br/>
<span class="kw">hence </span><a NAME="E4:79"/>
<span class="p1">(<span class="default"><font color="Maroon" title="c2">a</font> <a href="topgrp_1.html#K1" title="TOPGRP_1:func.1">*</a></span>)</span> <a href="tops_2.html#K2" title="TOPS_2:func.2">/"</a>  is  <a href="pre_topc.html#V5" title="PRE_TOPC:attr.5">continuous</a> 
 ; <a class="txt" onmouseover="tooltip.show('hs',this)" onmouseout="tooltip.hide()" onclick="hs(this)" href="javascript:()"><span class="comment"><font color="firebrick">::  thesis: </font></span></a><span class="hide"> verum</span><br/>


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